Multibend sensor

ABSTRACT

A multibend sensor is able to provide information regarding bending of the sensor data in a manner able to mitigate error propagation. A reference strip and a sliding strip are separated from each other by a spacer. Electrodes are located on the reference strip and the sliding strip. The bending of the multibend sensor will be reflected in the shifting of the sliding strip with respect to the reference strip and the measurements obtained from the electrodes.

This application claims the benefit of U.S. Provisional Application No.62/748,984 filed Oct. 22, 2018, the contents of which are incorporatedherein by reference. This application includes material which is subjectto copyright protection. The copyright owner has no objection to thefacsimile reproduction by anyone of the patent disclosure, as it appearsin the Patent and Trademark Office files or records, but otherwisereserves all copyright rights whatsoever.

FIELD

The disclosed apparatus and methods relate to the field of sensing, andin particular to providing accurate determination of positioning using asensor.

BACKGROUND

In the past, sensing gloves have been employed to detect hand gestures.An example is the Dataglove, set forth in U.S. Pat. No. 5,097,252, whichemployed optical bend sensors along the fingers to detect fingerposition. Nintendo's Power Glove used a similar design, but withresistive bend sensors. In both cases, the bend sensors were not verysensitive, providing only a single measure of the overall bend for eachbend sensor.

Bend sensors are used in applications beyond finger and hand sensing.They are often employed to understand human motion more generally.Additionally, bend sensors are used in robotics, sensing deformation instructures and space suit monitoring.

To better understand position of systems with multiple joints, somesystems have used a bend sensor per joint, or at each point ofarticulation. There are challenges with this approach that limit itspracticality. For example, the bend sensors have to be custom fitted forthe spacing between joints. The need for fitting for the spacing can beproblematic for tracking human motion because of size variation inpeople.

Additionally, there is the problem of cascaded error from the jointmeasurements. For example, the angle of each successive segment of afinger may be determined as the sum of the joint angles to that segment.Thus, any errors in the angle measurements taken for each of thepreceding joints accumulate. This is why robot arms use extremely highprecision angular encoders to find a modestly precise position.Unfortunately, inexpensive bend sensors have poor angular precisionmaking them inadequate for understanding the impacts of cascaded jointerror.

Systems have attempted to overcome this shortcoming by using cameras andother sensing techniques to directly measure finger positions.Camera-based techniques are challenged by the difficulty of finding goodviewpoints from which to view what is happening. Other position sensorsystems can be bulky and/or expensive. Inertial tracking can be used butit has severe drift issues.

Additionally there are Fiber Bragg Grating sensors that permit measuringbends along the length of a fiber bundle and can recover detailed shapesof a particular geometry. These sensors are difficult to make andrequire significant, bulky instrumentation and complex calibration.Further, they are expensive and impractical for most applications.

Therefore, there is a need for an improved method and apparatus foraccurately determining bending through the use of sensors.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features, and advantages of thedisclosure will be apparent from the following more particulardescription of embodiments as illustrated in the accompanying drawings,in which reference characters refer to the same parts throughout thevarious views. The drawings are not necessarily to scale, emphasisinstead being placed upon illustrating principles of the disclosedembodiments.

FIG. 1 shows a top down view of a sensor strip.

FIG. 2 shows a bottom up view of a sensor strip.

FIG. 3 is a schematic view of sliding and reference sensor strip.

FIG. 4 is diagram illustrating a reference strip wrapped around aspacer.

FIG. 5 is another diagram of a reference strip wrapped around a spacer.

FIG. 6 is another view of a sensor strip formed from a sliding strip anda reference strip.

FIG. 7 is a diagram illustrating the calculations of a segment.

FIG. 8 is a diagram illustrating using a linear segment analysis for thecurves.

FIG. 9 is a diagram illustrating the determination of angles in thelinear segment analysis.

FIG. 10 is a diagram illustrating the spaced electrodes.

FIG. 11 is a diagram illustrating a multiplanar multibend sensor.

FIG. 12 is a diagram of a multibend sensor employing triangularelectrodes and rectangular electrodes.

FIG. 13 is another diagram of a multibend sensor employing triangularelectrodes and rectangular electrodes further illustrating connections.

FIG. 14 is a diagram of a multibend sensor employing triangularelectrodes and rectangular electrodes.

FIG. 15 is another diagram of a multibend sensor employing triangularelectrodes and rectangular electrodes.

FIG. 16 is another diagram of a multibend sensor employing triangularelectrodes and rectangular electrodes.

FIG. 17 is a diagram showing the use of parallel strips with a camerachip.

FIG. 18 is a diagram showing an electrode pattern for a sensor that isable to determine wrapping.

FIG. 19 is a diagram of mechanical multibend sensor.

DETAILED DESCRIPTION

The present application describes various embodiments of sensors thatare designed for accurately determining the bending of a sensor. Themultibend sensor detects multiple bends along the length of the sensorand uses measurements taken to create an accurate determination of itscurrent shape. In an embodiment, the multibend sensor comprises twoflat, flexible strips. As used herein and throughout the application“strip” means a piece of material that is generally longer in onedimension than it is wide. A strip may be rectangular shaped,cylindrical shaped, or generally have an amorphous shape, provided onedimension is longer than the other. One of the strips is a referencestrip and the other strip is a sliding strip. While the strips arereferred to as reference strips and sliding strips it should beunderstood that the roles of reference strip and sliding strip areinterchangeable. The reference strip and the sliding strip are separatedby a spacer and mechanically joined on one end. The lengths of thereference strip and the sliding strip are substantially the same. Aplurality of retainers can ensure that the strips remain pressed againstthe spacer so that the distance between the strips remains substantiallyconstant when being used. At measurement points along the referencestrip, that can be determined by a variety of different methods, thecorresponding location on the sliding strip can be measured. When themultibend sensor is straight, the strips line up.

For example, a measurement point on a reference strip that is 1 cm fromthe attached end will align with a corresponding point on the slidingstrip that is also at 1 cm when the strips are not bent. But if themultibend sensor is bent into a circular arc, or other bent shape, thestrips will slide relative to each other. The inner strip in the arcwill be along a smaller radius than the outer strip. Even though thestrips are the same length, they will cover a different angular extant.With the strip conjoined on one end, the tighter the arc, the more theother ends will slide relative to each other, moving the free ends ofthe strips further apart. The multibend sensor works by measuring theserelative shifts at many points along the sensor using capacitiveelectrodes or another suitable measuring method. By using the dataacquired by the measuring method during the bending event, it ispossible to determine the shape of the multibend sensor. This is trueeven in the case of multiple bends along the multibend sensor.

Unlike previous systems that measured angles independently at multiplepoints, by measuring the relative shift, it can be shown thatmeasurement errors at one point do not impact the understanding of theangles at other points. This makes the multibend sensor less sensitiveto measurement error. By measuring at many points the relative shiftbetween flexible strips as they are bent into a complex fashion, theshape of the multibend sensor can be determined. Unlike the previoussystems that measured angles independently at multiple points therebyaccumulating error, by measuring shift, measurement errors at one pointdo not impact the understanding of absolute angle at other points. Thismakes the present invention less sensitive to measurement errors.

Referring now to FIGS. 1 and 2, shown is an embodiment of a multibendsensor 10. FIG. 1 shows a schematic side view of the multibend sensor10. FIG. 2 shows a top and a bottom view of the multibend sensor 10. Inthe embodiment shown, the multibend sensor 10 has a sliding strip 12 anda reference strip 14. The sliding strip 12 is secured to the referencestrip 14 at a distal end 16 of the reference strip 14. In the embodimentshown there is a spacer 18 located between the sliding strip 12 and thereference strip 18. Additionally shown are retainers 22 that retain thesliding strip 12 and the reference strip 14 against the spacer 18.

Operably connected to the sliding strip 12 and the reference strip 14 iscircuitry 24 that is adapted to receive and process measurements thatoccur. In the embodiment shown, the circuitry 24 may comprisecomponents, or be operably connected to components, such as processors,signal generators, receivers, etc.

The sliding strip 12 and the reference strip 14 may be formed fromflexible printed circuit board strips. While the sliding strip 12 andthe reference strip 14 are shown having specific electrode patterns, itshould be understood that the roles of each of the respective strip maybe changed and that the sliding strip 12 may function as the referencestrip 14 and vice versa depending on the particular implementation.Electrodes 20 may be placed on the surfaces of the sliding strip 12 andthe reference strip 14. The electrodes 20 are adapted to transmit andreceive signals. The electrodes 20 may be arranged in any pattern thatis capable of determining a change during the bending of the slidingstrips 12 and the reference strip 14. Additionally, the number, size andshape of the electrodes 20 implemented on sliding strip 12 and thereference strip 14 may be changed based on a particular implementation.

Still referring to FIGS. 1 and 2, the sliding strip 12 and the referencestrip 14 are flexible and able to move and bend. Additionally the spacer18, which is placed between the sliding strip 12 and the reference strip14, is flexible and able to move and bend. In an embodiment, the spacer18 may have different levels of flexibility with respect to the slidingstrip 12 and the reference strip 14. In an embodiment, the sliding strip12, the reference strip 14 and the spacer 18 may each have differentlevels of flexibility. In an embodiment, there is no spacer 18 and thesliding strip 12 and the reference strip 14 move with respect to eachother.

The spacer 18 used in the embodiments preferably keeps the strips spacedat a constant distance regardless of the amount of bending, yet stillpermits relative sliding. Spacer 18 preferably has a thickness that isable to permit there to be difference between the lengths of the slidingstrip 12 and the reference strip 14 when there is bending. In anembodiment, there may be no spacer and the sliding strip 12 and thereference strip 14 may be abutting each other, however there shouldstill be sufficient distance between the outward facing sides to permitssensing of the relative shift between the sliding strip 12 and thesliding strip 14 during a bend. In an embodiment, the spacer 18 may havethe same flexibility as the sliding strip 12 and the reference strip 14.A thick spacer 18 will provide a good amount of shift, but the spacer 18itself may change thickness with a tight bend. A thin spacer 18 willhave this issue less but may not provide adequate shifting. In anembodiment, the spacer 18 may be made out of a series of thin layerswhich slide against each other. This allows a thick spacer 18 to havefairly tight bends without changing overall thickness.

Having a known spacing between the reference layer and sliding layers isassists in obtaining accurate data. Ensuring the spacing can beaccomplished by different methods. As discussed above with respect toFIG. 1, retainers 22 can be affixed to one strip and provide compressiveforce to the other strip that slides against it as shown. The retainers22 may be plastic or elastic pieces that provide a compressive force tothe reference strip 14 and the sliding strip 12. The compressive forceshould be such that it maintains the distance but does not inhibitmovement of the reference strip 14 and the sliding strip 12. In anembodiment, elastomeric sleeves can be used to achieve the same task,providing compressive force.

At the end portion 16, the sliding strip 12 and the reference strip 14are secured together. In an embodiment, the sliding strip 12 and thereference strip 14 are mechanically attached together. In an embodiment,the sliding strip 12 and the reference strip 14 are integrally securedto each together. In an embodiment, the sliding strip 12 and thereference strip 14 are secured at a location other than the distal end.In an embodiment, the sliding strip 12 and the reference strip 14 aresecured in the middle of the stip. Elsewhere along the lengths of thesliding strip 12 and the reference strip 14, the sliding strip 12 andthe reference strip 14 slide with respect to each other. The slidingstrip 12 and the reference strip 14 also slide against the spacer 18relative to each other. The retainers 22 ensure that the sliding strip12 and the reference strip 14 remain pressed against the spacer 18 so asto keep a constant distance between them. Circuitry 24 and electricalconnections between the strips are outside of the sensing area where thebending occurs. In the embodiment shown in FIGS. 1 and 2, the circuitry24 is located proximate to end portion 16 where the sliding strip 12 andthe reference strip 14 are joined. The sliding strip 12 and thereference strips 14 contain patterns of electrodes 20 that will allowthe electronics to detect the relative shift between the two strips atmany locations by measuring the coupling from electrodes 20 on thesliding strip 12 and the electrodes 20 on the reference strip 14 throughthe spacer 18.

The embodiment discussed above may be made using the materials andtechniques implemented to create flexible circuits. Flexible circuitsmay start with a flexible, insulating substrate such as polyimide. Athin conducting layer (such as copper, silver, gold, carbon, or someother suitably conducting material) is adhered to the substrate with anadhesive. In an embodiment, the conducting layer is patterned usingphotolithographic techniques. In an embodiment, the conducting layer isapplied by sputtering. In an embodiment, the conducting layer is appliedby printing. When applied via printing, conductive ink can be directlypatterned onto the substrate.

Similar to rigid printed circuit boards (PCBs), flexible circuits can bemanufactured to include multiple conductive layers, separated byinsulators. Vias may provide connections among the different layers.Like rigid PCBs, standard electrical components may be affixed toflexible circuits using soldering and other well-known techniques.However, because some components are not flexible, flexing theirattachments may lead to broken electrical connections. For this reason,flexible circuits may employ stiffeners in the area of components, sothat that the region of the circuit does not appreciably flex. Forsimilar reasons, flexible circuits tend not to place vias in regionsthat are actually bending since the stresses in those areas maysometimes lead to breakage.

Many electrode patterns for the multibend sensor can benefit from theuse of interlayer connections in bending regions. Dupont® has developedspecial conductive inks that are explicitly designed to withstandrepeated flexure. However other suitable flexible conductive inks may beused as well. These inks can be implemented in the multibend sensorsdiscussed herein. Flexible inks permit flexible connections betweenconductive layers, serving the role of vias. It should be noted thatthese flexible conductive inks are compatible with a wide range ofsubstrates, including fabric. This allows for the construction ofmultibend sensors that are directly integrated into clothing.Additionally, in an embodiment clothing is made from fibers thatfunction as multibend sensors. When implementing multibend sensor fibersstiffeners may be added in order to restrict the movement of themultibend sensor fibers.

Referring now to FIGS. 3-5, when the multibend sensor is wrapped aroundan object in a circle, the inner of the two strips conforms to thecircle, while the outer strip conforms to a slightly larger circle dueto the thickness of the spacer 18. Because the two strips have differentradii of curvature, the unconstrained ends will not align with eachother. By knowing the length of the strips, sliding strip 12 andreference strip 14 and the thickness of the spacer 18, the radii candirectly be calculated. If the relative shift between the two strips atmany places is measured a model of the bend as a series of circular arcscan be constructed. This provides a much better understanding of theshape of the bend as opposed to traditional sensors.

Still referring to FIGS. 3-5, to illustrate the way in which themultibend sensor works, take two strips of length L, the sliding strip12 and the reference strip 14 separated by a spacer 18 of thickness t.The sliding strip 12 and the reference strip 14 are joined together atone end and cannot move relative to one another at that end. When thereference strip 14 is wrapped into a circle of radius r as shown in FIG.4, the reference strip 14 will have a radius of curvature of r, whilethe sliding strip 12 will have a smaller radius of r−t.

The circumference of the circle is 2πr. The reference strip 14, which isof length L, covers a fraction of the circle:

$\frac{L}{2\pi \; r}$

To put it in terms of radians, angle subtended by this strip is:

$\theta_{r} = \frac{L}{r}$

As shown in the diagram, when curled in the direction of the thicknessmeasurement t, the sliding strip 12 ends up on the inside, with asmaller radius of curvature. The tighter wrap means that some of thesliding strip 12 extends beyond the end of the reference strip 14. Ifthis continues along a circle of the same radius, the sliding strip 12subtends an angle of:

$\theta_{s} = \frac{L}{r - t}$

The end of the reference strip 14 lines up with a corresponding point onthe inner sliding strip 12. To give a more precise definition, it is theintersection point on the sliding strip 12 to the normal constructedthrough the endpoint of the reference strip 14.

This point can be found on the sliding strip 12 by finding thedifference in the angular extent of the two arcs, finding the extendinglength s_(s) and subtracting this from the total length L.

${\theta_{r} - \theta_{s}} = {{\frac{L}{r} - \frac{L}{\left( {r - t} \right)}} = \frac{Lt}{r\left( {r - t} \right)}}$

The length of the segment s_(s) of the sliding strip 12 that extendspast the sliding strip 12 can be found by dividing the angular extent inradians by 2π to find the fraction of the circle and multiplying by thecircumference.

$s_{s} = {{\frac{Lt}{r\left( {r - t} \right)}\frac{1}{2\pi}2{\pi \left( {r - t} \right)}} = {L\frac{t}{r}}}$

Solving these equations for the radius r gives:

$r = {t\; \frac{L}{s_{s}}}$

By measuring the relative shift between the strips, the radius ofcurvature across the length can be calculated using this simpleequation.

Now consider the case where bending occurs in a clockwise direction asshown in FIG. 5.

The analysis proceeds much as before, but now the sliding strip is onthe outside, with a radius of curvature of r+t.

$\theta_{r} = \frac{L}{r}$ $\theta_{s} = \frac{L}{r + t}$

As before, the goal is to locate the point on the sliding strip 12 thatcorresponds to the endpoint of the reference strip 14. However, becausethe sliding strip 12 is on the outside and thus subtends a smaller anglethe arc has to be continued to find the intersecting point. s_(s) iscalculated by finding the angle subtended and the corresponding lengthon the sliding strip.

${\theta_{r} - \theta_{s}} = {{\frac{L}{r} - \frac{L}{\left( {r + t} \right)}} = \frac{Lt}{r\left( {r + t} \right)}}$$s_{s} = {{\frac{Lt}{r\left( {r + t} \right)}\frac{1}{2\pi}2{\pi \left( {r + t} \right)}} = {L\; \frac{t}{r}}}$

This is the same result as obtained in the counterclockwise case. Thedifference here is that s_(s) in the first case is the amount thesliding strip 12 extended past the reference strip 14, and in this case,it is the amount extra that would be needed to reach the end of thereference strip 14.

To combine these two cases, consider the radius of curvature to be asigned quantity, with a positive r indicating an arc which proceeds in acounterclockwise direction and a negative r indicating a clockwisedirection.

A new variable, L_(s) is defined as the total length along the slidingstrip 12 to line up with the end of the reference strip 14. The signedradius of curvature is:

$r = {t\; \frac{L}{L - L_{s}}}$

In FIG. 4, L_(s)<L, gave a positive radius of curvature. In FIG. 5,L_(s)>L, gives a negative radius of curvature. The signed radius ofcurvature is then used to find the signed angular extent of thereference strip.

$\theta_{r} = {\frac{L}{r} = \frac{L - L_{s}}{t}}$

In the following, all angles and radii of curvature are signed.

Reconstructing the Curve from Shift Measurements

In an embodiment, the multibend sensor models shape as a series ofcircular arcs of different radii to allow for complex curves. Bymeasuring the relative shift at many points along the strips, thecurvature of each segment can be quickly determined.

The multibend sensor 10 shown in FIG. 6 comprises a sliding strip 12 anda reference strip 14. Finding the shape of the reference strip 14 is thegoal. At fixed intervals along the reference strip the correspondingshifted position along the sliding strip 12 is measured. Bycorresponding, it is meant that points that lie at the same angle withrespect to the common center of the radius of curvature are used.Another way to say this is that if a normal to the curve of thereference strip 14 is constructed at the measurement point, ameasurement will be made where it intersects the sliding strip 12.

L_(r)[n] is the length of the reference strip 14 to measurement point n.L_(s)[n] is the length of the sliding strip 12 to measurement point n.

A segment that spans from n to n+1 on both the reference strip 14 andsliding strip 12 is provided as an example. On the side of the referencestrip 14, the segment begins at L_(r)[n] and ends at L_(r)[n+1].Similarly, the corresponding sliding strip 12 extends from L_(s)[n] toL_(s)[n+1]. The signed radius of curvature and the signed angular extentof the reference strip 14 segment can be found.

Recalling that:

$r = {t\; \frac{L}{L - L_{s}}}$ $\theta_{r} = \frac{L - L_{s}}{t}$

It can be seen that:

${r\lbrack n\rbrack} = {t\; \frac{{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}}{\left( {{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}} \right) - \left( {{L_{s}\left\lbrack {n + 1} \right\rbrack} - {L_{s}\lbrack n\rbrack}} \right)}}$${\theta_{r}\lbrack n\rbrack} = \frac{\left( {{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}} \right) - \left( {{L_{s}\left\lbrack {n + 1} \right\rbrack} - {L_{s}\lbrack n\rbrack}} \right)}{t}$

A series of circular arcs of known length, angular extent, and radius ofcurvature is now known. This series can be pieced together to model thecomplete curve of the reference strip 14.

Consider a single arc as shown in FIG. 7. A starting angle ϕ[n] and anending angle ϕ[n+1] which are tangent to the arc at its endpoints can bedetermined. It can be presumed that sequential segments connectsmoothly—i.e. that the derivative is continuous at the point ofconnection. This is why the connection points are described by a singletangent angle.

The arc begins at a known starting point, (x[n], y[n]), and at aninitial known angle of ϕ[n] and proceeds to an unknown ending point,(x[n+1], y[n+1]), at an unknown ending angle of ϕ[n+1]. The change inangle from starting point to the ending point is just the turning of thesegment angle.

ϕ[n+1]=ϕ[n]+θ_(r)[n]

To find the x, y translation, the increment in x and y over the arc isadded to the previous point. For convenience, the center of the radiusof curvature of the arc is considered to be at the origin and used tocalculate endpoint positions. The difference in these is then applied tothe known starting point.

For this calculation, the angles from the center that form the arc areknown. The normal to ϕ[n] is

${\varphi \lbrack n\rbrack} - {\frac{\pi}{2}.}$

For an arc or positive radius of curvature, this gives the anglepointing out from the center of the radius of curvature. If the radiusof curvature is negative, it points in the opposite direction. Thisresults in a sign flip that is corrected by using the signed radius ofcurvature. The endpoints can then be found iteratively via theseequations:

${x\left\lbrack {n + 1} \right\rbrack} = {{x\lbrack n\rbrack} + {{r\lbrack n\rbrack}{\cos \left( {{\varphi \left\lbrack {n + 1} \right\rbrack} - \frac{\pi}{2}} \right)}} - {{r\lbrack n\rbrack}{\cos \left( {{\varphi \lbrack n\rbrack} - \frac{\pi}{2}} \right)}}}$${y\left\lbrack {n + 1} \right\rbrack} = {{y\lbrack n\rbrack} + {{r\lbrack n\rbrack}{\sin \left( {{\varphi \left\lbrack {n + 1} \right\rbrack} - \frac{\pi}{2}} \right)}} - {{r\lbrack n\rbrack}{\sin \left( {{\varphi \lbrack n\rbrack} - \frac{\pi}{2}} \right)}}}$

These equations can be slightly simplified using trig identities.

x[n+1]=x[n]+r[n](sin(ϕ[n+1])−sin(ϕ[n]))

y[n+1]=y[n]+r[n](cos(ϕ[n])−cos(ϕ[n+1]))

These equations describe the series of circular arcs that model thebend. A circular arc is typically described by its center (C_(x)[n],C_(y)[n]), its radius of curvature r[n], a starting angle, and anangular extent θ_(r)[n].

The center of an arc segment can be found by starting at (x[n], y[n]),and following the radius to the arc center (C_(x)[n], C_(y)[n]). Thestarting angle is found from the normal at the point (x[n], y[n]), whichis

${\varphi \lbrack n\rbrack} - {\frac{\pi}{2}.}$

The center is then:

${C_{x}\lbrack n\rbrack} = {{{x\lbrack n\rbrack} + {{r\lbrack n\rbrack}{\cos \left( {{\varphi \lbrack n\rbrack} - \frac{\pi}{2}} \right)}}} = {{x\lbrack n\rbrack} + {{r\lbrack n\rbrack}{\sin \left( {\varphi \lbrack n\rbrack} \right)}}}}$${C_{y}\lbrack n\rbrack} = {{{y\lbrack n\rbrack} + {{r\lbrack n\rbrack}{\sin \left( {{\varphi \lbrack n\rbrack} - \frac{\pi}{2}} \right)}}} = {{y\lbrack n\rbrack} - {{r\lbrack n\rbrack}{\cos \left( {\varphi \lbrack n\rbrack} \right)}}}}$

Note that the use of the signed radius of curvature ensures followingthe normal to the center.

The starting angle is:

$\left( {{\varphi \lbrack n\rbrack} - \frac{\pi}{2}} \right){{sign}\left( {r\lbrack n\rbrack} \right)}$

The sign is needed to flip the angle if the arc proceeds clockwise. Theextent of the arc is θ_(r)[n], which is also a signed value.

Sensitivity to Measurement Error

Any real measurement of shift will be imperfect, making it important tounderstand how measurement errors impact the accuracy of the modelledcurve. In jointed arms, noisy measurements of joint angles quicklyaccumulate, causing significant errors in the final position of the endeffector. Measurement errors in the multibend sensor are more forgiving.

Consider the case of a single shift measurement error at the nth point.Compared to the ideal, the shifted point will cause an error in theradii of curvature of two adjacent segments. The error on one segmentwill be one direction, while the error on the other segment will be inthe opposite direction, tending to cancel things out to first order.This property, of segment errors tending to create somewhat compensatingerrors holds in general and is a consequence of the shift measurementswhich give the total accumulated shift to that point.

To show the sensitivity to error, take the example of two successivesegments with the coordinates:

x[0]=0,y[0]=0),(x[1],y[1]),(x[2],y[2])

Ideal measurements for L_(r)[n] and L_(s)[n]are given. However, L_(s)[1]will be perturbed by a measurement error of δ. How this error propagatesto (x[2], y[2]) is then found.

In the unperturbed case (and noting that ϕ[0]=0):

x[1] = x[0] + r[n](sin (φ[1]) − sin (0)) = x[0] + r[n]sin (φ[1])y[1] = y[0] + r[n](cos (0) − cos (φ[1])) = y[0] + r[n](1 − cos (φ[1]))${r\lbrack n\rbrack} = {t\; \frac{{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}}{\left( {{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}} \right) - \left( {{L_{s}\left\lbrack {n + 1} \right\rbrack} - {L_{s}\lbrack n\rbrack}} \right)}}$${\theta_{r}\lbrack n\rbrack} = \frac{\left( {{L_{r}\left\lbrack {n + 1} \right\rbrack} - {L_{r}\lbrack n\rbrack}} \right) - \left( {{L_{s}\left\lbrack {n + 1} \right\rbrack} - {L_{s}\lbrack n\rbrack}} \right)}{t}$φ[n + 1] = φ[n] + θ_(r)[n]

Equally spaced measurement points, 1 unit apart are presumed.

L _(r)[n+1]−L _(r)[n]=1 for all n

Apostrophes are used to indicate the variables for the case withmeasurement error δ at L_(s)[1]. This allows the resulting angles withand without mid-point measurement error to be.

$\mspace{20mu} {{r\lbrack 0\rbrack} = {t\; \frac{1}{1 - \left( {L_{s}\lbrack 1\rbrack} \right)}}}$$\mspace{20mu} {{r^{\prime}\lbrack 0\rbrack} = {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}}}$$\mspace{20mu} {{r\lbrack 1\rbrack} = {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack}} \right)}}}$$\mspace{20mu} {{r^{\prime}\lbrack 1\rbrack} = {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack} - \delta} \right)}}}$$\mspace{20mu} {{\theta_{r}\lbrack 0\rbrack} = \frac{1 - {L_{s}\lbrack 1\rbrack}}{t}}$$\mspace{20mu} {{\theta_{r}^{\prime}\lbrack 0\rbrack} = \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t}}$$\mspace{20mu} {{\theta_{r}\lbrack 1\rbrack} = \frac{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack}} \right)}{t}}$$\mspace{20mu} {{\theta_{r}^{\prime}\lbrack 1\rbrack} = \frac{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack} - \delta} \right)}{t}}$  φ[0] = 0$\mspace{20mu} {{\varphi \lbrack 1\rbrack} = {{\theta_{r}\lbrack 0\rbrack} = \frac{1 - {L_{s}\lbrack 1\rbrack}}{t}}}$$\mspace{20mu} {{\varphi^{\prime}\lbrack 1\rbrack} = {{\theta_{r}^{\prime}\lbrack 0\rbrack} = \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t}}}$${\varphi \lbrack 2\rbrack} = {{{\varphi \lbrack 1\rbrack} + {\theta_{r}\lbrack 1\rbrack}} = {{\frac{1 - {L_{s}\lbrack 1\rbrack}}{t} + \frac{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack}} \right)}{t}} = \frac{2 - {L_{s}\lbrack 2\rbrack}}{t}}}$${\varphi^{\prime}\lbrack 2\rbrack} = {{{\varphi^{\prime}\lbrack 1\rbrack} + {\theta_{r}^{\prime}\lbrack 1\rbrack}} = {{\frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right\rbrack}{t} + \frac{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack} - \delta} \right)}{t\;}} = \frac{2 - {L_{s}\lbrack 2\rbrack}}{t}}}$

This shows that the ending angle after two arcs is unimpacted by amisreading in the middle point. The angle error does not propagate.

The error in the point locations are considered.

  x[n + 1] = x[n] + r[n](sin (φ[n + 1]) − sin (φ[n]))  y[n + 1] = y[n] + r[n](cos (φ[n]) − cos (φ[n + 1]))$\mspace{20mu} {{x\lbrack 1\rbrack} = {{{r\lbrack 0\rbrack}\left( {\sin \left( {\varphi \lbrack 1\rbrack} \right)} \right)} = {t\; \frac{1}{1 - \left( {L_{s}\lbrack 1\rbrack} \right)}\sin \; {\sin \left( \frac{1 - {L_{s}\lbrack 1\rbrack}}{t} \right)}}}}$$\mspace{20mu} {{y\lbrack 1\rbrack} = {{{r\lbrack 0\rbrack}\left( {1 - {\cos \left( {\varphi \lbrack 1\rbrack} \right)}} \right)} = {t\; \frac{1}{1 - \left( {L_{s}\lbrack 1\rbrack} \right)}}}}$$\mspace{20mu} {{x^{\prime}\lbrack 1\rbrack} = {{{r^{\prime}\lbrack 0\rbrack}\left( {\sin \left( {\varphi^{\prime}\lbrack 1\rbrack} \right)} \right)} = {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}\sin \; {\sin \left( \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t} \right)}}}}$$\mspace{20mu} {{y^{\prime}\lbrack 1\rbrack} = {{{r^{\prime}\lbrack 0\rbrack}\left( {1 - {\cos \left( {\varphi^{\prime}\lbrack 1\rbrack} \right)}} \right)} = {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}}}}$${x\lbrack 2\rbrack} = {{{x\lbrack 1\rbrack} + {{r\lbrack 1\rbrack}\left( {{\sin \left( {\varphi \lbrack 2\rbrack} \right)} - {\sin \left( {\varphi \lbrack 1\rbrack} \right)}} \right)}} = {{t\; \frac{1}{1 - \left( {L_{s}\lbrack 1\rbrack} \right)}\sin \; {\sin \left( \frac{1 - {L_{s}\lbrack 1\rbrack}}{t} \right)}} + {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack}} \right)}\left( {{\sin \left( \frac{2 - {L_{s}\lbrack 2\rbrack}}{t} \right)} - {\sin \left( \frac{1 - {L_{s}\lbrack 1\rbrack}}{t} \right)}} \right)}}}$${y\lbrack 2\rbrack} = {{{y\lbrack 1\rbrack} + {{r\lbrack 1\rbrack}\left( {{\cos \left( {\varphi \lbrack 1\rbrack} \right)} - {\cos \left( {\varphi \lbrack 2\rbrack} \right)}} \right)}} = {{t\; \frac{1}{1 - \left( {L_{s}\lbrack 1\rbrack} \right)}} + {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack}} \right)}\left( {{\cos \left( \frac{1 - {L_{s}\lbrack 1\rbrack}}{t} \right)} - {\cos \left( \frac{2 - {L_{s}\lbrack 2\rbrack}}{t} \right)}} \right)}}}$${x^{\prime}\lbrack 2\rbrack} = {{{x^{\prime}\lbrack 1\rbrack} + {{r^{\prime}\lbrack 1\rbrack}\left( {{\sin \left( {\varphi^{\prime}\lbrack 2\rbrack} \right)} - {\sin \left( {\varphi^{\prime}\lbrack 1\rbrack} \right)}} \right)}} = {{t\; \frac{1}{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}\sin \; {\sin \left( \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t} \right)}} + {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack} - \delta} \right)}\left( {{\sin \left( \frac{2 - {L_{s}\lbrack 2\rbrack}}{t} \right)} - {\sin \left( \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t} \right)}} \right)}}}$${y^{\prime}\lbrack 2\rbrack} = {{{y^{\prime}\lbrack 1\rbrack} + {{r^{\prime}\lbrack 1\rbrack}\left( {{\cos \left( {\varphi^{\prime}\lbrack 1\rbrack} \right)} - {\cos \left( {\varphi^{\prime}\lbrack 2\rbrack} \right)}} \right)}} = {{t\; \frac{1}{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}} + {t\; \frac{1}{1 - \left( {{L_{s}\lbrack 2\rbrack} - {L_{s}\lbrack 1\rbrack} - \delta} \right)}\left( {{\cos \left( \frac{1 - \left( {{L_{s}\lbrack 1\rbrack} + \delta} \right)}{t} \right)} - {\cos \left( \frac{2 - {L_{s}\lbrack 2\rbrack}}{t} \right)}} \right)}}}$

Using these equations, the endpoint error under different conditions canbe plotted. It is clear that position error at the end of the firstsegment is somewhat compensated for by an oppositely signed error in thenext segment.

While the embodiment and examples discussed above uses arcs inperforming the analysis, other measurement techniques and analyses maybe employed. In an embodiment, ellipses are used for approximating thecurves. In an embodiment, analysis of the may be performed usingparabolas. In an embodiment, splines are used for approximating a curve.In an embodiment, a polynomial function is used for approximating thecurve. In an embodiment, all of the methodologies discussed herein areused in approximating the curve.

Another possible model of a curve is to represent it as a series ofconnected straight linear segments.

Referring to FIGS. 8 and 9, for a piecewise linear model, the bends arepresumed to be perfectly sharp, and occur only at fixed intervals on areference strip 84. The sliding strip 82 will be presumed to conform toa fixed distance from the reference strip 84. This will createcorresponding sharp bends for each bend of the reference strip 84.Bending towards the reference strip 84 will mean that extra length willbe needed on the sliding strip 82 to conform to the new shape.Similarly, bending towards the sliding strip 82 will take less length toconform.

The calculation is begun by calculating the extra length required on thesliding strip 82 given a bend toward the reference strip 84. Lookingtowards FIG. 9, the multibend sensor has a bend of angle A. Thevertically opposite angle is also A. The extra length of the slidingstrip 82 needed to conform to the bend is shown as 2s. The two bendpoints bisect the bend angle. The vertically opposite angle is also A/2.With the right angle construction, the A−90 angle is found bysubtracting the right angle. Finally the angle opposite s is computer asA/2−(A−90). The tangent of this angle is equal to the opposite sidelength (s) divided by the adjacent side length (t).

tan(A/2−(A−90))=s/t

s=t*tan(90−A/2)

s=t*cot(A/2)

And for the total length added:

2s=2t*cot(A/2)

This formula is also correct for when the bend angle exceeds 180, andbends up towards the sliding strip 82. In this case the additionallength is negative.

For convenience, the bending angle, B, can be defined relative to nobend being 0.

B=180−A

A=180−B

Substituting in:

s=t*tan(90−B/2)=t*tan(90−(180−B)/2)=t*tan(B/2)

2s=2t*tan(B/2)

Given a measurement of shift, the angle that would have given rise to itis calculated.

B=2 arctan(s/t) where s is the half shift.

Like the circular arc model, this piecewise linear model still has thegeneral behavior of measurement error in one shift measurement creatinga complimentary error in the next, partially canceling out the impact ofpotential additive error.

Consider an ideal measurement vs one where there is measurement error inthe first segment.

Ideal measurements: s1 and s2Measurements with error: s1+d, s2−d

B1=2 arctan(s1/t)

B2=2 acrtan(s2/t)

The resulting angle of the last segment is simply the sum of the angleto that point.

Btotal=B1+B2=2 arctan(s1/t)+2 arctan(s2/t)

Repeating the calculation with measurement error:

Btotal_err=2 arctan(s1/t+d/t)+2 arctan(s2/t−d/t)

These total bends are not the same, however, it can be shown via seriesexpansion around d=0 that the errors cancel to first order.

Physical Implementations

The mechanism of measuring shift between two bending members with fixedspacing can be accomplished using different sensing techniques inconjunction with the reference strip and the sliding strips.

Capacitive Sensing Techniques

Capacitive sensing can be used with a multibend sensor and is themethodology discussed above with respect to FIGS. 1-3. Electrodes can bepatterned on standard flexible printed circuit boards (PCB) whencreating the reference strip and the sliding strip. The capacitancethrough the spacer can be measured, and relative position determined.For example, looking to FIG. 10, a pattern of interdigitated electrodes20 allows one to perform differential measurements by comparing thecapacitance of overlapping electrodes 20 to determine relative shift.The differential nature of this measurement makes it highly insensitiveto various types of error. In addition to the electrode pattern shown inFIG. 10, other electrode patterns can be implemented that will furtherprovide measurements that can help determine the overall movement andshape of the multibend sensor.

Still referring to FIG. 10, a plurality of the electrodes 20 are adaptedto transmit signals and a plurality of the electrodes 20 are adapted toreceive signals from the electrodes 20 that are transmitting signals. Inan embodiment, the electrodes 20 adapted to transmit signals and theelectrodes 20 adapted to receive signals may be switched or alternateddepending on the implementations. In an embodiment, an electrode 20adapted to transmit a signal may at a different time also be adapted toreceive a signal. Received signals are used in order to determinemovement of one strip with respect to the other strip.

In an embodiment, orthogonal frequency division multiplexing can be usedwith a multibend sensor employing a plurality of electrodes 20 that areadapted to receive and transmit orthogonal signals. In an embodiment,unique frequency orthogonal signals are used. In an embodiment, a uniquefrequency orthogonal signal is transmitted on each of the electrodes 20that is transmitting. Electrodes 20 that are adapted to receive signalmay receive the transmitted signals and process them in order to obtaininformation regarding the relative shift of the reference strip withrespect to the sliding strip. This can then be used to determine theshape of the curve formed by the multibend sensor.

In general, the curvature of multiple dimensions can be determined byforming a mesh of reference strips and sliding strips with eachmultibend sensor determining its own respective curve. After the curveof each multibend sensor is determined the entire curvature of a planecan be modeled. In an embodiment, a plurality of multibend sensors maybe placed on a three dimensional object that is subject to variousdeformation across its 3D surface. The plurality of multibend sensorsmay be able to accurately determine the curving deformation of a 3Dobject after reconstructing curvature taken from each of the multibendsensors.

In another embodiment, the strips are replaced with fibers that areflexible in 3 dimensions. These fibers are then packed around a centralreference fiber such that the outer sliding fibers move relative to thereference fiber when bent. In embodiment, spacers maintain a constantspacing between all the fibers. The relative shifts can be measured by avariety of means, including via patterned electrodes along the fiber.

In an embodiment the sensor may be created from narrow sheets that moreclosely resemble a flexible wire, being able to flex outside of theplane. If two of these devices are held together, sensing in orthogonaldirections, flexing in and out of the plane can be measured.

Another embodiment is shown in FIG. 11. This embodiment provides amultibend sensor 110 that is able to determine curvature in more thanone planar direction. There is a sliding plane 112 and a reference plane114. In FIG. 11 the planes are not shown on top of each other however itshould be understood that this is for ease of viewing the planes slidingplane 112 and the reference plane 114 are positioned with respect toeach other in a similar manner in which the strips discussed above arepositioned. Electrodes 115 are placed on the sliding plane 112 and thereference plane 114. In FIG. 11, the electrodes 115 are formed as rowsand columns. In an embodiment, the electrodes are formed as pads. In anembodiment, the electrodes are formed as dot antennas. There mayadditionally be a spacer plane placed between the sliding plane 112 andthe reference plane 114 in order to establish a distance between thesliding plane 112 and the reference plane 114. In an embodiment, thereference plane 114 and the sliding plane 112 are implemented without aspacer layer with the electrodes are 115 placed on the outward facingsurfaces with the substrates of the planes functioning as a spacerlayer. Furthermore, while there may be electrodes 115 placed on bothplanes, there may be transmitting electrodes placed on the sliding plane112 and the reference plane 114 and receiving electrodes located at aninterstitial region between the two planes. Also, the electrodes 115 canbe either transmitting or receiving.

Still referring to FIG. 11, the sliding plane 112 and the referenceplane 114 are flexible planes that are able to bend. The reference plane114 and the sliding plane 112 are attached at various attachment points.Attachment points may be located at any location between the planesprovided that they establish a reference location by which to ascertainthe movement of one plane with respect to the other. In an embodiment,the attachment point may be the center location of the planes. In anembodiment, there are more than one attachment point from which relativemovement of the planes is established. In an embodiment the planes aresecured to each other at an edge. In an embodiment, the planes aresecured at multiple points along the edge. In an embodiment, the planesare secured at points along an edge and within the area of the planes.

Turning to FIGS. 12 and 13, another embodiment of a capacitive electrodedesign to measure relative shift is shown. While multilayer flexcircuits are widely available, there are certain limitations to designthat may be imposed. A common restriction is to not allow vias onbending sections. Therefore, patterns which do not require interlayerconnections in bending areas are sometimes preferred.

FIG. 12 shows two triangular electrodes 120 that form the referencestrip 124, and a series of rectangular electrodes 121 formed on thesliding strip 122. By measuring the relative capacitance to the Aelectrode 120 to the capacitance to the B electrode 120 for each of therectangular electrodes 120 on the sliding strip 122, the relativeposition of the rectangular electrodes 120 can be determined.

This pattern shown in FIGS. 12 and 13 does not require multiple layerconnections. On the reference strip 124, connections can be directlymade from either end. The rectangular electrodes 121 on the slidingstrip 122 can be made via bus 126 as shown in FIG. 13. In an embodiment,shielding can be employed around the rectangular electrodes 121 and thetriangular electrodes 120. Shielding can assist in mitigatinginterference. Electrodes that are transmitting can be surrounded byground and receiving electrodes can be driven with an active shield inorder to mitigate interference.

The design shown in FIGS. 12 and 13 is sensitive to slight rotationsbetween the reference strip 124 and the sliding strip 122. For example,if the spacing is greater on the top versus the bottom, it may cause asystematic error. This can be corrected by calibration. Sensitivity canalso be ameliorated by using a less sensitive pattern.

An example of a pattern with reduced sensitivity is shown in FIG. 14.The pattern shown in FIG. 14 employs additional triangular electrodes141 placed on the reference strip 144. Rectangular electrodes 141 areplaced on the sliding strip 142. The electrode pattern shown in FIG. 14is symmetric about the centerline of the reference strip 144. Thisreduces the sensitivity as compared to the pattern shown in FIG. 12. Thereduced sensitivity occurs because the triangular electrode 141 isfurther away on one side and closer on the other side. This distanceroughly balances out the impact of any tilt that may exist.

FIG. 15 shows another embodiment of sensor electrodes. FIG. 15 shows anarrangement of a reference strip 154 and sliding strip 152. Thereference strip 154 has a plurality of triangular electrodes 150. Thesliding strip 152 has a plurality of rectangular electrodes 151. Incomparison to the electrode pattern shown in FIG. 12, the pattern inFIG. 15 replicates that arrangement of triangular electrodes 150. Theangled pattern is replicated on a smaller scale in the neighborhood ofeach measurement to improve resolution. The sensor pattern shown in FIG.15 can also be combined with shielding and symmetry techniques.

FIG. 16 shows another embodiment of sensor electrodes. FIG. 16 shows anarrangement of a reference strip 164 and sliding strip 162. Thereference strip 164 has a plurality of triangular electrodes 160. Thesliding strip 162 has a plurality of rectangular electrodes 161. Incomparison to the electrode pattern shown in FIG. 12, the pattern inFIG. 16 replicates that arrangement of triangular electrodes 160. Theangled pattern is replicated on a smaller scale in the neighborhood ofeach measurement so as to improve resolution. The sensor pattern shownin FIG. 16 can also be combined with shielding and symmetry techniques.When shifting causes a rectangular electrode 161 to get near the end ofa triangular electrode 160, some nonlinearity will result. A way toaddress this is to use multiple sets of the triangular electrodes 160.The sets are shifted so that when a rectangular electrode 161 is near anedge on one triangular electrode 160, it is not at an edge on another ofthe triangular electrode 160.

Optical

In addition to capacitive based sensing, multibend sensors can becreated using optical techniques rather than capacitive. Instead ofinterdigitated electrodes, optical transmitters and receivers can beused. Signals can be transmitted through an optically transmissivespacer located between a reference strip and sliding strip. Waveguidetechniques permit the electronics to be placed at one end, rather thandistributing them along the sensor.

Using standard flex circuit techniques, it is possible to place standardelectro-optic components such as LEDs and photodiodes on a flexiblestrip. However, because these components are not in and of themselvesflexible, local stiffening at the measurement point may be needed.Certain techniques may be used to work around the issue of localstiffening. In general, flexible electronics can be applied to themanufacture of multibend sensors (e.g. doing local electric fieldsensing, and reporting data back via a shared bus). In particular, theavailability of OLEDs and other optic devices in a flexible form makesit possible to build distributed optical encoders along a flexiblestrip.

Flexible waveguides may also be employed to bring the optical signal toand from the measurement points distributed along the strips. In thisway, the optoelectronics can be gathered at one location. For examplethe optoelectronics can be placed at the end where the strips arejoined. At this location a rigid PCB can hold the electro-opticcomponents.

Additionally, to cut down on the required number of optical connections,multiplexing techniques can be employed. For example, each senselocation could employ optical filters so that different colors of light,different polarizations, or some combination of these are active atdifferent locations along the multibend sensors, and can bedistinguished at the end with the opto-electronics.

These systems have a path for light to travel from one strip to theother. This can be accommodated several different ways. In anembodiment, the spacer may be made from transparent materials. In anembodiment, slots may be provided in the neighborhood of the measuringspots. In an embodiment, the spacer may maintain an air gap between thestrips. In an embodiment, the optical fibers may have nicks that permitlight to bleed from one cable to another. In an embodiment, there may bebundles of optical fibers that are tied in the middle wherein therelative shift of both ends of the bundles are able to be determined.

Referring to FIG. 17, inexpensive camera chips also can be used to makemultibend sensors. These chips could be used at various points along thestrips so as to measure shift. Still referring to FIG. 17, multiple,parallel sliding strips 172 are used that attach to a reference strip174 at staggered attachment points 176. The ends of these sliding strips172 can then extend to be observed by a camera chip 175. A single cameracan thus track the motion of multiple slide strips 172 with highprecision, effectively giving the same result as measuring the shift atdifferent locations.

While flexible electronics are an option, there are other options fordistributing optoelectronics along a flexible strip. In an embodiment, arigid PCB may be attached to a flexible strip via elastic members. Inthis way, the strip can still bend freely, while the floatingelectro-optic module looks toward the encoder markings on the otherflexible strip. To help maintain alignment, the electro-optic module canbe designed to have a larger optical area that looks through a smalleraperture in the flexible strip. Even if the rigid PCB slightly wiggleswith respect to the strip, the measurement will always be done withrespect to the aperture in the strip.

When sensing shift, there is a question of how much shift must one sensebefore running out of range. Looking to the arrangement of receivingelectrodes 182 and transmitting electrodes 184 shown in FIG. 18 anexample of shifting range can be explained. In this case, there are asmall number of receiving electrodes 182 that are placed on a slidingstrip, and a larger number of transmitting electrodes 184 placed on areference strip. Instead of providing unique signals on everytransmitting electrode 184, signals are reused periodically. Each of thenumbered transmitting electrodes 184 representing a different signal. Ifthe shift is limited to the region of one set of transmitting electrodes184, the position can be uniquely determined. If the shift is greaterthan this, the shift reading is not uniquely determined by the closesttransmitting electrode 184. In this instance it could have shifted somuch as to have wrapped into the next set of transmitting electrodes184. Because a sequence of measurements is made along the strips, thecombined shift from earlier segments can be seen and is likely toindicate that a wrap has occurred. Because incremental unwrapping canoccur, the constraint is not on any particular receiving electrode 182staying within range of one set of transmitting electrodes 184. It isonly limited by the ability to unwrap. If it is known that the number oftransmitting electrodes 184 between successive receiving electrodes 182is limited to +/−half the number of receiving electrodes 182 nominallybetween transmitting electrodes 184 one can uniquely determine theposition of the next segment because it is known which transmittingelectrodes 184 could be within range of the previous segment. Moresophisticated techniques can extend this even further for example, bymaking assumptions about higher order derivatives. Although thistechnique is explained in the context of a capacitive sensor, the sametechnique can be applied to other embodiments. Using the opticalmultistrip setup, instead of just detecting an end, the strip can haverepeated variations which are detected and analyzed to find a preciseposition. It is possible to use calibration targets with many edges toallow the positions to be determined by combining data all of them.

Other Methodologies

Above, capacitive and optical techniques were discussed, however, othermechanisms may be employed. For example, similar to a potentiometer, onestrip can serve as a distributed resistor, and the other may havemultiple wipers that make contact at numerous points along the resistivestrip. The voltage at each wiper can be arranged to indicate therelative position along the resistive strip. A resistive strip islocated on one strip, and a voltage placed across it. This creates avoltage gradient along the strip that is position dependent. Wipersalong the top strip make sliding contact with the strip, sensing thevoltage at their location. The wrapping detection discussed above can beachieved by having a separate potentiometer formed in the region of eachwiper to allow more precise measurements. Mechanically, the wipers couldalso play a role in maintaining the spacing between the layers sincethey are spacers in and of themselves.

An improvement on the above design is rather than having a singleresistive stripe along the strip, separate ones may be placed in theneighborhood of each wiper. Then each smaller resistive stripe couldhave the entire voltage gradient over a much smaller displacement,greatly increasing the resolution of the measurement. It should be notedthat the number of connections to the strip with the resistive stripesis still only two.

Rather than mechanical wipers, other methods can be employed to createshift-dependent resistivity changes. For example, magneto-resistivematerials change resistance in the presence of a magnetic field. Aresistive trace, running parallel to a conductor could be effectivelybridged at different locations including magneto-resistive materialbetween these traces, which can be selectively made more conductive by amagnet on the other strip.

Another embodiment employs a series of magnets on one strip and Halleffect sensors on the other in order to measure shift. Time domaintechniques may also be utilized to measure length. Time domainreflectometry techniques in either the electrical, optical or acousticdomain can be used to measure shift at multiple points. To use these,the measurement points create a path for signal to return.Magnetostrictive position transducer methods may also be used to measureshift.

In an embodiment, inductive proximity sensing can be employed. Theinductance of a coil will change in response to certain materials beingwithin proximity to them. For example, in an embodiment, one stripcarries a series of coils, while the other has sections of differentmagnetic permeability that are detected by the coils. The detection canbe done a number of ways, including noting the change in inductance ofeach coil independently, or looking for the change in coupling amongdifferent coils. It is also possible to have coils on both strips, andmeasure the coupling between them. Linear Variable DifferentialTransformers (LVDTs) can be straightforwardly applied to this type ofmeasurement.

In an embodiment, electromagnetic coupling can be utilized using radiofrequency (RF) coupling between the strips.

In an embodiment, multibend sensors are designed for remoteinterrogation via RF. A simple tank circuit (LC) is used where eitherthe L or C are dependent on the relative shift between strips. This typeof circuit can be created on the strips using only patterning ofconductive material. The resonant frequency of the tank circuit isdependent on relative shift, and can be read remotely using standardRFID techniques. The strips can be designed so as to contain multipleresonances that are each dependent on the local relative shift. If theresonances are reasonably separated in frequency, a remote frequencyscan can reveal the change in each resonance independently. With theaddition of active components, other techniques, such as time domainmultiplexing can be employed to read the shift over multiple points.

Magnetic sensors (Hall effect, Giant Magnetoresistive, etc.) can be usedto measure local magnetic field. A pattern of magnetization of one stripcould be detected on the other to determine relative shift at manypoints. Magnetic circuits can be employed to bring the flux measurementto a convenient physical location. High magnetic permeability materialserves to channel the flux similar to a conductive wire carryingelectric current. Using these techniques, a number of magnetic sensorscan be positioned on the conjoined end of the strips, makingmeasurements at various points along the strips.

Magnetostrictive transducers have been employed for measuring positionin harsh industrial environments. The position of a moving magnet isdetermined by pulsing current in a magnetostrictive element, whichcauses a mechanical impulse to be generated in the element in the regionof the magnet. The time for this impulse to propagate back to ameasurement point is a function of the position of the magnet. In anembodiment, magnets are placed on one strip, and magnetostrictivematerial is placed on the other.

Analogous techniques can be employed using photoconductive materials. Alight on the sliding strip can shift the location of bridging. Thiscould be an LED or other light source mounted on the strip, or a simpleaperture through which a separate light source is allowed to selectivelypass.

Some of the measurement error propagation properties of the multibendsensor can be obtained on more traditional arm/encoder systems throughmechanical means. Parallel linkages are often used to maintain theparallelity of two members.

FIG. 19, shows three sets of parallel linkages that guarantee that thehorizontal lines remain parallel to each other. The dots representencoders. The angle measured at each encoder is always with respect tothe top line. In this way, measurement errors at each encoder do notpropagate in measuring the absolute exit angle at each encoder. Variouscombinations of gears, belts and other linkages can be employed tosimilar effect.

The above discussed multibend sensors provide curvature data along itslength. This data can be used in more sophisticated ways to give moredetailed models. For example, one can interpolate or fit a higher orderfunction to model the change in curvature along the sensor, and thuscreate a model with effectively many more segments. One could alsochange the underlying model of a segment from a circular arc to adifferent functional form.

The above described embodiments of the multibend sensor can accuratelydetermine the shape of a curve or curved surface. Some applications ofthis technique may be in determining the positioning of roboticssystems. In an embodiment the multibend sensor is used for pliableinterfaces. In an embodiment the multibend sensor is used for humanjoint motion rehabilitation. In an embodiment the multibend sensor isused for human joint motion in virtual reality. In an embodiment, themultibend sensor is used for determining curvature of a back, movementof a head, or bending of legs. In an embodiment the multibend sensor isused for measuring complex curves. In an embodiment the multibend sensoris used for complex vibration understanding and active control. In anembodiment the multibend sensor is used for automotive, tires and seatdeformation. In an embodiment the multibend sensor is used for posturemonitoring. In an embodiment the multibend sensor is used for expressivemusical instrument interfaces. In an embodiment the multibend sensor isused for tank/pressure bladder monitoring for deformations such asbubbling out (e.g. monitoring planes, submarines etc.).

The multibend sensor may also be used in understanding the shape of apressurized system. For example, airplanes with pressurized cabinsundergo significant stress and deformation as they are repeatedlypressurized and depressurized. If a particular area becomes weakenedthrough repeated stress, it will begin to bubble out (or in depending onwhich side you are looking at) relative to other areas. The multibendsensor is employed so as to detect this for understanding the rate ofsystem fatigue, and where failures may be imminent. Submarines, holdingtanks, and all sorts of pressurized containers have similar issues thatcan benefit from the application of the multibend sensor. In anembodiment, the multibend sensor is used in assisting with oil and gasexploration when determining the curvature of bits.

Other mechanical systems that deform under load can also benefit fromthe multibend sensor. Another advantage of the multibend sensorsdescribed above is that the precision arises from geometricrelationships rather than from electrical properties that aresusceptible to changes due to environmental condition and are subject toaging and wear, this makes the disclosed multibend sensors suitable formonitoring bridges, support beams, etc. over the life of the structure.

Another advantage of the multibend sensors described above is that theprecision arises from geometric relationships rather than fromelectrical properties that are susceptible to changes due toenvironmental condition and subject to aging and wear. Implementationsof this application may employ principles used in implementingorthogonal frequency division multiplexing sensors and other interfacesdisclosed in the following: U.S. Pat. Nos. 9,933,880; 9,019,224;9,811,214; 9,804,721; 9,710,113; and 9,158,411. Familiarity with thedisclosure, concepts and nomenclature within these patents is presumed.The entire disclosure of those patents and the applications incorporatedtherein by reference are incorporated herein by reference. Thisapplication may also employ principles used in fast multi-touch sensorsand other interfaces disclosed in the following: U.S. patent applicationSer. Nos. 15/162,240; 15/690,234; 15/195,675; 15/200,642; 15/821,677;15/904,953; 15/905,465; 15/943,221; 62/540,458, 62/575,005, 62/621,117,62/619,656 and PCT publication PCT/US2017/050547, familiarity with thedisclosures, concepts and nomenclature therein is presumed. The entiredisclosure of those applications and the applications incorporatedtherein by reference are incorporated herein by reference.

As used herein, and especially within the claims, ordinal terms such asfirst and second are not intended, in and of themselves, to implysequence, time or uniqueness, but rather, are used to distinguish oneclaimed construct from another. In some uses where the context dictates,these terms may imply that the first and second are unique. For example,where an event occurs at a first time, and another event occurs at asecond time, there is no intended implication that the first time occursbefore the second time, after the second time or simultaneously with thesecond time. However, where the further limitation that the second timeis after the first time is presented in the claim, the context wouldrequire reading the first time and the second time to be unique times.Similarly, where the context so dictates or permits, ordinal terms areintended to be broadly construed so that the two identified claimconstructs can be of the same characteristic or of differentcharacteristic. Thus, for example, a first and a second frequency,absent further limitation, could be the same frequency, e.g., the firstfrequency being 10 Mhz and the second frequency being 10 Mhz; or couldbe different frequencies, e.g., the first frequency being 10 Mhz and thesecond frequency being 11 Mhz. Context may dictate otherwise, forexample, where a first and a second frequency are further limited tobeing frequency-orthogonal to each other, in which case, they could notbe the same frequency.

While the invention has been particularly shown and described withreference to a preferred embodiment thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the spirit and scope of theinvention.

1. A multibend sensor comprising: a reference strip, wherein thereference strip has placed thereon a first plurality of electrodes,wherein each of the first plurality of electrodes transmits a signal,wherein the reference strip is adapted to flexibly move in at least onedimension; a sliding strip, wherein the sliding strip has placed thereona second plurality of electrodes, wherein the sliding strip is securedto a portion of the reference strip, wherein the sliding strip isadapted to flexibly move in at least one dimension in the same directionas the reference strip when the reference strip moves; and circuitryoperably connected to the first plurality of electrodes and the secondplurality of electrodes, wherein measurements determined from the firstplurality of electrodes and the second plurality of electrodes are usedto determine information regarding the bends of the multibend sensor. 2.The sensor of claim 1, further comprising a spacer placed between thereference strip and the sliding strip.
 3. The sensor of claim 1, whereinthe portion of the reference strip to which the sliding strip is securedis a distal end of the reference strip.
 4. The sensor of claim 1,wherein measurements determined from the first plurality of electrodesand the second plurality of electrodes are analyzed by determining arcsformed during movement of the reference strip and the sliding strip. 5.The sensor of claim 1, wherein measurements determined from the firstplurality of electrodes and the second plurality of electrodes areanalyzed by determining linear segments formed during movement of thereference strip and the sliding strip.
 6. The sensor of claim 1, whereinthe reference strip is one of a plurality of reference strips and thesliding strip is one of a plurality of sliding strips.
 7. The sensor ofclaim 6, wherein the plurality of reference strips and the plurality ofsliding strips form a mesh structure.
 8. The sensor of claim 6, whereinthe plurality of reference strips and the plurality of sliding stripsform a plurality of layers.
 9. The sensor of claim 1, further comprisinga plurality of retainers securing the sliding strip and the referencestrip to a spacer.
 10. The sensor of claim 1, wherein the firstplurality of electrodes are formed as complementary triangularelectrodes.
 11. A sensor comprising: a reference strip, wherein thereference strip has placed thereon a first plurality of electrodes; asliding strip, wherein the sliding strip has placed thereon a secondplurality of electrodes, wherein the sliding strip is secured to aportion of the reference strip; and circuitry operably connected to thefirst plurality of electrodes and the second plurality of electrodes,wherein measurements determined from the first plurality of electrodesand the second plurality of electrodes are used to determine informationregarding bending of the sensor.
 12. The sensor of claim 11, furthercomprising a spacer placed between the reference strip and the slidingstrip.
 13. The sensor of claim 11, wherein the portion of the referencestrip to which the sliding strip is secured is a distal end of thereference strip.
 14. The sensor of claim 11, wherein the portion of thereference strip to which the sliding strip is secured is located in thecenter of the reference strip.
 15. The sensor of claim 11, whereinmeasurements determined from the first plurality of electrodes and thesecond plurality of electrodes are analyzed by determining arcs formedduring bending of the sensor.
 16. The sensor of claim 11, wherein thereference strip is one of a plurality of reference strips and thesliding strip is one of a plurality of sliding strips.
 17. The sensor ofclaim 16, wherein the plurality of reference strips and the plurality ofsliding strips form a mesh structure.
 18. The sensor of claim 16,wherein the plurality of reference strips and the plurality of slidingstrips form a plurality of layers.
 19. The sensor of claim 11, furthercomprising a plurality of retainers securing the sliding strip and thereference strip to a spacer.
 20. The sensor of claim 11, wherein thefirst plurality of electrodes are formed as complementary triangularelectrodes.